Question

The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is greater than 1". Let B be the event "the outcome is greater than or equal to 2". Find P(A or B). Outcome Probability 1 0.33 2 0.19 3 0.13 4 0.31 5 0.04

Answer 1

Let A and B be the following events:

`\begin{gathered} A=\mleft\lbrace x>1\mright\rbrace \\ B=\mleft\lbrace x\ge2\mright\rbrace \end{gathered}`

first, we can find the probability of event A:

`\begin{gathered} P(x>1)=P(2)+P(3)+P(4)+P(5) \\ =0.19+0.13+0.31+0.04=0.67 \end{gathered}`

then, the probability of event B is:

`\begin{gathered} P(x\ge2)=P(2)+P(3)+P(4)+P(5) \\ =0.19+0.13+0.31+0.04=0.67 \end{gathered}`

notice that both probabilities are the same, so, the events must be the same too. Therefore, P(A or B) = 0.67